Use asymptotes to match $f(x)=\frac{4 x^{2}}{x^{2}+1}$ with its graph.

Question

Use asymptotes to match  $f(x)=\frac{4 x^{2}}{x^{2}+1}$ with its graph.

Quizplus · Accepted Answer

The vertical asymptotes are given by the zeros of the denominator, which are $x=\pm i$. These are represented in the graph by the dashed lines. The horizontal asymptote is found by dividing the leading term of the numerator by the leading term of the denominator, which gives $y=4x^2/x^2=4$ as a horizontal asymptote. This is represented by the solid line. Choice B accurately displays these asymptotes and matches the graph of the function.

Use Asymptotes to Match f(x)=4x2x2+1f(x)=\frac{4 x^{2}}{x^{2}+1}f(x)=x2+14x2​ With Its Graph

Use Asymptotes to Match $f(x)=\frac{4 x^{2}}{x^{2}+1}$ With Its Graph